Accuracy,
resolution and repeatability: the critical selection factors
for speed and position measurementDespite their frequent
use, the terms accuracy, resolution and repeatability are often
misunderstood. As critical factors in the selection of position
and speed sensors, engineers must ensure they fully understand
the terminology, says Mark Howard, General Manager at Zettlex
Ltd.

When sourcing
and selecting sensors and other precision measuring instruments,
many engineers still don't understand the terms accuracy, resolution
and repeatability.

The terminology
applied to instrumentation can be confusing but is critical when
it comes to selecting the right measuring instruments for an
application - especially for position and speed transducers.
Get this part wrong and engineers could end up paying more than
they need to for over-specified sensors. Conversely, a product
or control system may lack critical performance if the position
or speed sensor does not meet the specification.

First, some
important definitions:

An instrument's
Accuracy is a measure of its
output's veracity.
An instrument's Resolution is a measure of the
smallest increment or decrement in position that it can measure.
A position measuring instrument's Precision is its degree of reproducibility.
A position measuring instrument's Linearity is a measurement of the deviation
between a transducer's actual output to the perfect slope of
displacement versus output.

To most intents
and purposes, linearity is tantamount to accuracy, provided the
perfect slope - against which linearity is measured - passes
through a zero or datum position.

Most engineers
get confused about the differences between precision and accuracy.
Using the analogy of an arrow fired at a target, accuracy describes
the closeness of an arrow to the bullseye.

If many arrows
are fired, precision equates to the size of the arrow cluster.
If all arrows are grouped together, the cluster is considered
precise.

A perfectly
linear measuring device is also perfectly accurate.

So, that's
pretty straightforward then - as long as you specify very accurate
and very precise measuring instruments every time, you'll be
OK. Unfortunately, there are snags to this approach. First, high
accuracy, high precision instrumentation is always expensive.
Second, high accuracy, high precision instrumentation may require
careful installation and this may not be possible due to vibration,
thermal expansion/contraction, etc. Third, certain types of high
accuracy, high precision instrumentation are also delicate and
will suffer malfunction or failure if there are changes in environmental
conditions - most notably temperature, dirt, humidity and condensation.

The optimal
strategy is to specify what is required - nothing more, nothing
less. In a displacement transducer in an industrial flow meter
for example, linearity will not be a key requirement because
it is likely that the fluid's flow characteristics will be non-linear.
More likely, repeatability and stability over varying environmental
conditions are the key requirements.

In a CNC machine
tool, it is likely that accuracy and precision will be key requirements.
Therefore, a displacement measuring instrument with high accuracy
(linearity), resolution and high repeatability even in dirty,
wet environments over long periods without maintenance, are key
requirements.

A good tip
is always to read the small print of any measuring instrument's
specification - especially about how the claimed accuracy and
precision varies with environmental effects, age or installation
tolerances.

Another useful
tip is to find out exactly how an instrument's linearity varies.
If this variation is monotonic and slowly varying, the non-linearity
could be easily calibrated out using a few reference points.
For example, for a gap measuring device this could be achieved
using some slip gauges. In the example below, a fairly non-linear
transducer is calibrated in to a highly linear (accurate) device
with a relatively low number of reference points.

However, in
this second example, a rapidly varying device is calibrated with
10 points and its linearity hardly changes. It might take >1000
points for such a rapidly varying measurement characteristic
to be linearised. Such a process is unlikely to be practical
with slip gauges but it might be practical to compare the readings
in a lookup table against a higher performance reference device
such as a laser interferometer.

A common
pitfall - optical encoders
Optical encoders work by shining a light source onto or through
an optical element - usually a glass disk. The light is either
blocked or passes through the disk's gratings and a signal, analogous
to position, is generated.

The glass disks
have tiny features that allow manufacturers to claim high precision.
What is often not explicit is what happens if these tiny features
are obscured by dust, dirt, grease, etc. In reality, even very
small amounts of foreign matter can cause mis-reads. There is
seldom any warning of failure - the device simply stops working
altogether and suffers from 'catastrophic failure'. What is less
well known is the issue of accuracy in optical encoders and optical
encoder kits.

Consider an
optical device using a 1" nominal disk with a resolution
of 18 bits (256k points). Typically, the claimed accuracy for
such a device might be +/-10 arc-seconds. However, what should
be in big bold print (but surprisingly never is) is that the
stated accuracy assumes that the disk rotates perfectly relative
to the read head and that temperature is constant.

If we consider
a more realistic example, the disk is mounted slightly eccentrically
by 0.001" (0.025mm).

Eccentricity
comes from several sources, including the following: Concentricity of the glass disk
on its hub. Concentricity of the hub's through
bore relative to the optical disk. Perpendicularity of the hub relative
to the plane of the optical disk. Parallelism of the optical disk
face with the plane of the read head. Concentricity of the shaft on
which the hub is mounted. Clearances in the bearings and
bearing mounts, which support the main shaft. Imperfect alignment of the bearings. Roundness of the shaft and roundness
of the hub's through bore. Locating method (typically a
grub-screw will pull the hub to one side). Displacements due to stresses
or strain from forces on the shaft's bearings. Thermal effects.

A perfectly
mounted optical disk requires such fine engineering that cost
becomes prohibitive. In reality, there is a measurement error
because the optical disk is not where the read head thinks it
is. If we consider a mounting error of say 0.001", then
the measurement error is equivalent to the angle subtended by
0.001" at the optical track radius. To make the maths easy,
let's assume that the tracks are at a radius of 0.5".

This equates
to an error of 2 milliradians or 412 arc-seconds. In other words,
the device with a specification accuracy of 10 arc-seconds is
more than 40 times less accurate than its data sheet.

If you get
an optical disk to position accurately to within 0.001"
of an inch you are doing really well. Realistically, you're more
likely to be in the range 2-10 thousandths of an inch, so the
actual accuracy will be 80-400 times worse than you might have
originally calculated.

The measurement
principle of a resolver or a new generation inductive device
is completely different. Measurement is based on the mutual inductance
between the rotor (the disk) and the stator (reader). Rather
than calculating position from readings taken at a point, measurements
are generated over the full face of both the stator and rotor.
Consequently, discrepancies caused by non-concentricity in one
part of the device are negated by opposing effects at the opposite
part of the device. The headline figures of resolution and accuracy
are often not as impressive as those for optical encoders. However,
what's important here is that this measurement performance is
maintained across a range of non-ideal conditions.

The quoted
measurement performance of some of the new generation inductive
devices are not based on perfect alignment of rotor and stator
but realistically achievable tolerances (typically +/-0,2mm)
are accounted for in any quoted resolutions, repeatabilities
and accuracies. Furthermore, stated performance for inductive
devices are not subject to variation due to foreign matter, humidity,
lifetime, bearing wear or vibration.From a press release issued by Zettlex
(UK) Ltd.